Question: Find the greatest common factor of $63$ and $42$.
Explanation: The greatest common factor (GCF) is the largest number that is a factor of both $63$ and $42$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}63 &=3\cdot3\cdot7\\\\\\\\ 42&=2\cdot3\cdot7 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}63 &=3\cdot3\cdot7\\\\\\\\ 42&=2\cdot3\cdot7 \end{aligned}$ Each number shares the factors ${3}$ and ${7}$, so the GCF is $3\cdot7={21}$. The greatest common factor of $63$ and $42$ is $21$.